灵感来自this优秀的帖子我想使用帖子中使用的算法在 Clojure 中实现一个简单的表达式简化器。这篇文章提供了 F#、Scala、Haskell、C++ 和 Julia 的示例实现,它们都显得相当优雅。
我提出了两种不同的实现(见下文),但我有一种挥之不去的感觉,它们都不太惯用。
我的问题是:惯用的 Clojure 实现是什么样的?
第一次实现,主要基于协议(protocol):
(defprotocol Expr
(simplify1 [e])
(simplify [e]))
(defrecord Const [n]
Expr
(simplify1 [this] this)
(simplify [this] this))
(defrecord Variable [name]
Expr
(simplify1 [this] this)
(simplify [this] this))
(defrecord Add [l r]
Expr
(simplify1 [{:keys [l r] :as expr}]
(let [lclass (class l)
rclass (class r)]
(cond
(= lclass rclass Const)
(Const. (+ (:n l) (:n r)))
(and (= lclass Const) (= (:n l) 0))
r
(and (= rclass Const) (= (:n r) 0))
l
:else expr)))
(simplify [{:keys [l r]}]
(simplify1 (Add. (simplify l) (simplify r)))))
(defrecord Mult [l r]
Expr
(simplify1 [{:keys [l r] :as expr}]
(let [lclass (class l)
rclass (class r)]
(cond
(= lclass rclass Const)
(Const. (* (:n l) (:n r)))
(and (= lclass Const) (= (:n l) 0))
(Const. 0)
(and (= rclass Const) (= (:n r) 0))
(Const. 0)
(and (= lclass Const) (= (:n l) 1))
r
(and (= rclass Const) (= (:n r) 1))
l
:else expr)))
(simplify [{:keys [l r]}]
(simplify1 (Mult. (simplify l) (simplify r)))))
(defmulti print-expr class)
(defmethod print-expr Const [e]
(print-str (.value e)))
(defmethod print-expr ::expr [e]
(print-str "The expression cannot be simplified to a constant"))
(let [e (Add. (Mult. (Add. (Const. 1) (Mult. (Const. 0) (Variable. "X"))) (Const. 3)) (Const. 12))]
(-> e
simplify
print-expr))
第二个实现,主要基于多方法,并且比第一个更详细:
(defrecord Const [value])
(defrecord Variable [name])
(defrecord Add [l r])
(defrecord Mult [l r])
(derive Const ::expr)
(derive Variable ::expr)
(derive Add ::expr)
(derive Mult ::expr)
(defn sim-1-disp [{:keys [l r] :as e}]
(if (some #{(class e)} [Add Mult])
[(class e) (class l) (class r)]
(class e)))
(defmulti simplify class)
(defmulti simplify1 sim-1-disp)
(defmulti print-expr class)
(defmethod simplify Add [{:keys [l r]}]
(simplify1 (Add. (simplify l) (simplify r))))
(defmethod simplify Mult [{:keys [l r]}]
(simplify1 (Mult. (simplify l) (simplify r))))
(defmethod simplify ::expr [e]
e)
(defmethod simplify1 [Add Const Const] [{:keys [l r]}]
(Const. (+ (:value l) (:value r))))
(defmethod simplify1 [Add Const ::expr] [{:keys [l r] :as e}]
(if (= (:value l) 0)
r
e))
(defmethod simplify1 [Add ::expr Const] [{:keys [l r] :as e}]
(if (= (:value r) 0)
l
e))
(defmethod simplify1 [Mult Const Const] [{:keys [l r]}]
(Const. (* (.value l) (.value r))))
(defmethod simplify1 [Mult Const ::expr] [{:keys [l r] :as e}]
(cond (= (:value l) 0)
(Const. 0)
(= (:value l) 1)
r
:else e))
(defmethod simplify1 [Mult ::expr Const] [{:keys [l r] :as e}]
(cond (= (:value r) 0)
(Const. 0)
(= (:value r) 1)
l
:else e))
(defmethod simplify1 ::expr [e]
e)
(defmethod print-expr Const [e]
(print-str (.value e)))
(defmethod print-expr ::expr [e]
(print-str "The expression cannot be simplified to a constant"))
(let [e (Add. (Mult. (Add. (Const. 1) (Mult. (Const. 0) (Variable. "X"))) (Const. 3)) (Const. 12))]
(-> e
simplify
print-expr))
最佳答案
不确定是否是惯用的实现,但我认为正如 Guillermo Winkler 提到的那样,core.match
是一种非常自然的替代方法,尤其是 with variants 。正如您链接的文章所说,总和类型非常简洁。
(ns simplify
(:require [clojure.core.match :refer [match]]))
(defn- simplify-1 [expr]
(match expr
[::add [::const 0] a] a
[::add a [::const 0]] a
[::add [::const a] [::const b]] [::const (+ a b)]
[::mult [::const 0] _] [::const 0]
[::mult _ [::const 0]] [::const 0]
[::mult a [::const 1]] a
[::mult [::const 1] a] a
[::mult [::const a] [::const b]] [::const (* a b)]
_ expr))
(defn simplify [expr]
(match expr
[::add a b ] (simplify-1 [::add (simplify a) (simplify b)])
[::mult a b ] (simplify-1 [::mult (simplify a) (simplify b)])
_ (simplify-1 expr)))
示例:
(simplify [::add
[::mult
[::add [::const 1] [::mult [::const 0] [::var 'x]]]
[::const 3]]
[::const 12]])
;=> [:simplify/const 15]
这使您可以利用模式匹配来实现简洁,并具有与某些链接示例类似的优雅。不过,与您的协议(protocol)/多方法方法相比,这是有成本的 - 这些是可扩展的总和类型,包括通过其他人的代码而不触及您的源代码。这有多有用取决于您的应用程序。
一些旁白:
- 您还可以根据
clojure.walk/postwalk
定义simplify
,并将simplify-1
作为函数参数。这可能更容易扩展,因为simplify
不再需要知道哪些 expr 变体是操作,并且可以在对它们调用simplify-1
之外进行简化。 - 我尝试为此定义一个
core.typed
类型,但我的环境今天加载该类型时似乎出现一些问题,因此我无法检查它。
认为这应该或多或少合适:
(defalias Expr
"A variant type for algebraic expressions."
(Rec [e]
(U [(Value ::const) Number]
[(Value ::add) e e]
[(Value ::mult) e e]
[(Value ::var) Symbol])))
关于clojure - Clojure 中的惯用表达简化,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/31903623/